Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
166 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 18. C2×Q8×C97 | C8 | semidirect |
| 55. C97 | #1272 | semidirect |
| 66. C2×Q8 | #11715897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261601 | 2 |
| #20260642 | 2 |
| #1272 | 97 |